A die is tossed thrice. A success is defined | vedclass

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(A) For a binomial distribution,the mean is given by $\mu = np$ and the variance is given by $\sigma^2 = npq$.Here,the number of trials $n = 3$.The pr

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$\mu = 1, \sigma^2 = \frac{2}{3}$

Vedclass · Answer

(A) For a binomial distribution,the mean is given by $\mu = np$ and the variance is given by $\sigma^2 = npq$.Here,the number of trials $n = 3$.The probability of success $p$ (getting $1$ or $6$) is $p = \frac{2}{6} = \frac{1}{3}$.The probability of failure $q = 1 - p = 1 - \frac{1}{3} = \frac{2}{3}$.Calculating the mean:$\mu = np = 3 	imes \frac{1}{3} = 1$.Calculating the variance:$\sigma^2 = npq = 3 	imes \frac{1}{3} 	imes \frac{2}{3} = \frac{2}{3}$.Thus,the mean is $1$ and the variance is $\frac{2}{3}$.

$A$ die is tossed thrice. $A$ success is defined as getting $1$ or $6$ on a toss. Find the mean and the variance of the number of successes.

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